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Re: Simplification question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg110424] Re: Simplification question
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Thu, 17 Jun 2010 02:05:16 -0400 (EDT)

    (TrigToExp[ArcTanh[Tanh[a] Tanh[b]]] ==
        1/2 Log[(Exp[a+b]+Exp[-a-b])/(Exp[-a+b]+Exp[a-b])])
        //Simplify[#,Assumptions->{a\[Element]Reals,b\[Element]Reals}]&

True

On 6/15/2010 2:30 AM, Yaroslav Bulatov wrote:
> I'd like to verify that the following expression is true for a,b real.
> It seems to hold numerically.
>
> 1/2 Log[(Exp[a + b] + Exp[-a - b])/(Exp[-a + b] + Exp[a - b])] ==
> ArcTanh[Tanh[a] Tanh[b]]
>
> I tried Reduce and combinations of TrigToExp/Simplify with no luck,
> any suggestions?
>

-- 
Murray Eisenberg                     murrayeisenberg at gmail.com
80 Fearing Street                    phone 413 549-1020 (H)
Amherst, MA 01002-1912


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